In systems that transmit digital information in the form of analog signals, digital-to-analog conversion is required. Digital-to-analog converters (DACs) are typically relatively complex because they are capable of generating any arbitrary analog waveform from its corresponding digital representation.
Digital communication systems, such as digital cordless telephone systems, transmit digital data in the form of analog signals. In such systems the digital-to-analog (D/A) conversion process involves generating a small predetermined set of analog waveforms in response to the digital data that are to be transmitted. For example, a binary transmission scheme requires only two analog waveforms that correspond, respectively, to the rising and falling edges of the binary bit stream. In such a system, the D/A conversion process can be simplified to one that generates only the two required analog waveforms.
A binary digital signal has at times representing bits either a maximum value or a minimum value, denoting, respectively, a 1 or a 0. The signal preferably includes sharp, ideally instantaneous, transitions between these two values. This ensures that the signal will have attained its minimum or maximum value, as appropriate, at or near the start of the associated bit time, or bit position. Otherwise, the signal may be in between the maximum and minimum values at the bit times, which can lead to an incorrect assignment of bit values to the signal.
Ideally, the analog signals to which the binary signals are converted have the same sharp transitions. However, other constraints, such as constraints on the use of RF frequency, require that the transitions be smoothed.
In particular, wireless communications systems generally require that RF transmissions be contained within a specified frequency range, or channel. If the analog signal used to modulate the RF transmission includes the sharp transitions, it causes the RF transmission to occupy a wider frequency range, or bandwidth, that may exceed the specified frequency range. Accordingly, to avoid transmission problems, the systems typically spread or smooth the signal transitions in the time domain to limit the occupied frequency bandwidth. If, however, the transitions are spread too much, a receiver may have trouble detecting them within the prescribed bit times particularly in the presence of noise, and thus, it may assign incorrect bit values to the received signal.
One solution is to transmit analog signals with Gaussian shaped pulses. These pulses have smooth transitions, and thus, result in relatively narrow occupied frequency bandwidth. Further, the slopes of the transitions are relatively steep and easy to detect.
The problem with using Gaussian shaped pulses is producing them. Known prior systems that produce such pulses are costly. One example is an analog Gaussian filter that shapes the binary pulse in the continuous time domain. The filter is expensive because of component requirements and manufacturing alignments. Alternatively, a conventional D/A converter can be used. The system typically oversamples the input binary stream and, using lookup tables or by computation, determines the appropriate analog value of the pulse at each bit time of the oversampling clock. It then generates a signal with these values using a conventional D/A converter.